Entropy always increases in a closed system, but entropy within a system can be lowered if there is energy input from outside it. The “missing” entropy is then ejected into the outside system, often creating even more net entropy. If we had tiny nanobots that could attach themselves to specific molecules and move them, we could in principle separate the coffee and milk molecules that way. Once we’re finished and send the nanobots away, the nanobots would carry that extra entropy away with them (due to the machine parts slightly degrading from performing their action, building up waste heat in their circuits, and so on). So while the milk-coffee system would decrease in entropy, the milk-coffee-nanobot system would still have a net increase in entropy.
One common argument from pseudo-intellectual creationists is that life could not have arisen naturally because life is a very low entropy state compared to the original lifeless Earth. One only needs to point out that the Earth is not a closed system, as there is a source of energy providing Earth with the ability to reduce local entropy (hint: it’s that big bright thing in the sky).
I think it could happen in our very own universe, if you made sure the coffee and milk were both completely sterile and uncontaminated so that they wouldn’t spoil, and you could somehow keep it warm enough and pressurized so that it stayed in the liquid state. Given enough time, according to theory, it should return to its initial unstirred state.
At first I was thinking if you move the spoon and cup in exactly the opposite way (in terms of momentum) as the way you moved them when you stirred it, you’d end up with unstirred coffee.
But I’m not sure how much mixing is done by the heat radiation of the coffee/milk mix, or how much is done by the mix’s interactions at the molecular level with the cup and the air.
Not only that, but it’s not just the moving spoon doing the mixing, it’s the turbulence it causes - the edge of the spoon bowl sheds vortices which travel through the liquid, mixing it up along the way.
Precisely reversing the stirring action would not reverse this process - for two reasons - firstly (and most obviously) it would not cause vortices to arise in the liquid and find their way to the edges of the spoon, but also, stirring in reverse with the spoon is effectively just *stirring *forwards with a differently-shaped spoon (i.e. the profile of the spoon in one orientation vs another).
Right, that’s what I had in mind concerning the molecule-level interactions at the surface and with the cup. If those could be reversed, the vortices would appear in reverse. But reverse-stirring doesn’t accomplish that. So the answer to my question is, basically, the molecule-level interactions with the surface etc actually account for all of the mixing! (Just as the spoon does–because the two are just a single process seen at different times.)
You’d have to reverse all the molecule-level surface interactions, and move the spoon in precisely the reverse way than it originally moved (exactly reversing all accelerations etc). And time it perfectly. Not physically impossible, but even more outlandish than simply “stirring backwards.”